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Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups

Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite dimensional complex Hilbert space.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc6136
Date05 1900
CreatorsAtim, Alexandru Gabriel
ContributorsKallman, Robert, Bator, Elizabeth M., Lewis, Paul
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Copyright, Atim, Alexandru Gabriel, Copyright is held by the author, unless otherwise noted. All rights reserved.

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